Title of article :
Solvability and spectral properties of integral equations on the real line: I. Weighted spaces of continuous functions
Author/Authors :
Tilo Arens and Thorsten Hohage ، نويسنده ,
Issue Information :
دوهفته نامه با شماره پیاپی سال 2002
Pages :
27
From page :
276
To page :
302
Abstract :
We consider in this paper the solvability of linear integral equations on the real line, in operator form (λ − K)φ = ψ, where λ ∈ C and K is an integral operator. We impose conditions on the kernel, k, of K which ensure that K is bounded as an operator on X := BC(R). Let Xa denote the weighted space Xa := {χ ∈ X: χ(s) = O(|s|−a ) as |s| →∞}. Our first result is that if, additionally, |k(s, t)| κ(s − t), with κ ∈ L1(R) and κ(s) = O(|s|−b) as |s|→∞, for some b >1, then the spectrum of K is the same on Xa as on X, for 0 1. As an example where kernels of this latter form occur we discuss a boundary integral equation formulation of an impedance *boundary value problem for the Helmholtz equation in a half-plane.  2002 Elsevier Science (USA). All rights reserved
Journal title :
Journal of Mathematical Analysis and Applications
Serial Year :
2002
Journal title :
Journal of Mathematical Analysis and Applications
Record number :
930081
Link To Document :
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